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  • 1.
    Abbas, M.
    et al.
    University Pretoria, South Africa.
    De La Sen, M.
    University of the Basque Country, Spain.
    Nazir, Talat
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces2015Ingår i: Discrete dynamics in nature and society, ISSN 1026-0226, E-ISSN 1607-887X, Vol. 2015, artikel-id 532725Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

  • 2.
    Abbas, M.
    et al.
    Ton Duc Thang University, Ho Chi Minh City, Viet Nam.
    Nazir, Talat
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Popović, B.
    University of Kragujevac, Serbia.
    Radenović, S.
    University of Belgrade, Serbia.
    On Weakly Commuting Set-Valued Mappings on a Domain of Sets Endowed with Directed Graph2017Ingår i: Results in Mathematics, ISSN 1422-6383, Vol. 71, nr 3-4, s. 1277-1295Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The aim of this paper is to present coincidence and common fixed point results of set-valued mappings satisfying certain generalized graphic F-contractive conditions on a family of sets endowed with a graph. It is worth mentioning that these results are obtained without appealing to any form of continuity of mappings involved herein. Some examples are presented to support the results proved in this paper. Our results unify, generalize and extend various comparable results in the existing literature. © 2016, Springer International Publishing.

  • 3.
    Abbas, Mujahid
    et al.
    Ton Duc Thang Univ, Ho Chi Minh City, Vietnam..
    Nazir, Talat
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Lampert, Tatjana Aleksic
    Fac Sci, Dept Math, Radoja Domanovica 12, Kragujevac 34000, Serbia.
    Radenovic, Stojan
    State Univ Novi Pazar, Serbia..
    Common fixed points of set-valued F-contraction mappings on domain of sets endowed with directed graph2017Ingår i: Computational and Applied Mathemathics, ISSN 0101-8205, Vol. 36, nr 4, s. 1607-1622Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The aim of this paper is to present common fixed point results of set-valued graphic F-contraction mappings on a family of sets endowed with a graph. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

  • 4.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology.
    Qi, Xiaomin
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Linear and Nonlinear Classifiers of Data with Support Vector Machines and Generalized Support Vector Machines2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, s. 377-396Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    The support vector machine for linear and nonlinear classification of datais studied. The notion of generalized support vector machine for data classifications is used. The problem of generalized support vector machine is shown to be equivalent to the problem of generalized variational inequality and various results for the existence of solutions are established. Moreover, examples supporting the results are provided.

  • 5.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology.
    Qi, Xiaomin
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Linear Classification of data with Support Vector Machines and Generalized Support Vector Machines2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We showthat the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions. Moreover, we provide various examples to support our results.

  • 6.
    Nazir, Talat
    et al.
    COMSATS Institute of Information Technology, Abbottabad, Pakistan.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Common fixed point for integral type contractive mappings in multiplicative metric spaces2020Ingår i: Algebraic Structures and Applications / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rancic, Springer Nature, 2020, Vol. 317, s. 723-741Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    The fixed and common fixed point problems of selfmappings that are satisfying certain type generalized integral contractions in the setup of multiplicative metric spaces are investigated. Well-posedness results for fixed point problem of maps under restrictions of integral type contractions are obtained. Moreover, the periodic points results of generalized integral type contraction mappings are also obtained.

  • 7.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Common Fixed Point Results for Family of Generalized Multivalued F-contraction Mappings in Ordered Metric Spaces2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    In this paper, we study the existence of common fixed points of family of multivalued mappings satisfying generalized F-contractive conditions in ordered metric spaces. These results establish some of the general common fixed point theorems for family of multivalued maps.

  • 8.
    Nazir, Talat
    et al.
    Department of Mathematical Sciences, University of South Africa, South Africa.
    Silvestrov, Sergei
    Mälardalens universitet, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Fixed Point Results of Generalized Cyclic Contractive Mappings in Multiplicative Metric Spaces2022Ingår i: Stochastic Processes, Statistical Methods, and Engineering Mathematics, Springer Nature, 2022Konferensbidrag (Refereegranskat)
    Abstract [en]

    Several generalised contractive type conditions are established for existence, uniqueness and well-posedness of the fixed point results, limit shadowing property, and also for the property of coincidence of sets of periodic points and fixed points for cyclic contractive maps on multiplicative metric spaces. 

  • 9.
    Nazir, Talat
    et al.
    Department of Mathematical Sciences, University of South Africa, South Africa.
    Silvestrov, Sergei
    Mälardalens universitet, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Fixed Points of T-Hardy Rogers Type Mappings and Coupled Fixed Point Results in Multiplicative Metric Spaces2022Ingår i: Springer Proceedings in Mathematics and Statistics / [ed] Anatoliy Malyarenko, Ying Ni, Milica Rančić, Sergei Silvestrov, Springer Nature, 2022, Vol. 408, s. 343-365Konferensbidrag (Refereegranskat)
    Abstract [en]

    The fixed point results of T-Hardy Rogers type mappings that are satisfying generalized contractive conditions in the setup of multiplicative metric spaces are investigated. The well-posedness and limit shadowing property of T-Hardy Rogers type mappings are also established. Furthermore, periodic point property of these contraction mappings are also shown. Several examples are also presented to show the validity of main results.The coupled fixed point results are also obtained in multiplicative metric spaces. An application for solving integral equations are established in the frame work of multiplicative metric spaces.

  • 10.
    Nazir, Talat
    et al.
    Department of Mathematical Sciences, University of South Africa, South Africa.
    Silvestrov, Sergei
    Mälardalens universitet, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Some Periodic Point and Fixed Point Results in Multiplicative Metric Spaces2022Ingår i: Springer Proceedings in Mathematics and Statistics, Springer Nature, 2022, Vol. 408, s. 367-382Konferensbidrag (Refereegranskat)
    Abstract [en]

    We investigate the periodic points and common fixed point of generalized contraction mappings self-mappings in the setup of multiplicative metric spaces. We also study the well-posedness for the obtained results. The common fixed point results of mappings involved in the cyclic representation are also obtained. Moreover, some applications to obtain the common solution of integral equations are presented. 

  • 11.
    Nazir, Talat
    et al.
    Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa.
    Silvestrov, Sergei
    Mälardalens universitet, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Division of Mathematics and Physics, School of Education, Culture and Communication, Mälardalen University, P.O. Box 883, 72123 Västerås, Sweden.
    The Generalized Iterated Function System and Common Attractors of Generalized Hutchinson Operators in Dislocated Metric Spaces2023Ingår i: Fractal and Fractional, E-ISSN 2504-3110, Vol. 7, nr 12, artikel-id 832Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we present the generalized iterated function system for the construction of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors’ problems of rational contraction maps in the framework of dislocated metric spaces is also established. Moreover, the generalized collage theorem is also obtained in dislocated metric spaces.

  • 12.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Abbas, Mujahid
    Department of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore, Pakistan and Faculty of Science, Department of Mathematics, King Abdulaziz University, Saudi Arabia.
    Common fixed point results of four mappings in ordered partial metric spaces2016Ingår i: Waves Wavelets Fractals - Advanced Analysis, ISSN 2449-5557, Vol. 2, nr 1, s. 46-63Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    On partially ordered set equipped with a partial metric, we study the sufficient conditions for existence of common fixed points of various mappings satisfying generalized weak contractive conditions. These results unify several comparable results in the existing literature. We also study the existence of nonnegative solution of implicit nonlinear integral equation. Furthermore, we study the fractal of finite family of generalized contraction mappings defined on a partial metric space.

  • 13.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. COMSATS Institute of Information Technology, Pakistan.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Abbas, Mujahid
    Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa.
    Fractals of generalized F-Hutchinson operator2016Ingår i: Waves, Wavelets and Fractals. Advanced Analysis, ISSN 2449-5557, Vol. 2, nr 1, s. 29-40Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The aim of this paper is to construct a fractal with the help of a finite family of F−contraction mappings, a class of mappings more general than contraction mappings, defined on a complete metric space. Consequently, we obtain a variety of results for iterated function systems satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

  • 14.
    Nazir, Talat
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology, Pakistan.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Qi, Xiaomin
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Fractals of Generalized F-Hutchinson Operator in b-Metric Spaces2016Ingår i: Journal of Operators, ISSN 2314-5064, Vol. 2016, s. 9 pp-, artikel-id 5250394Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The aim of this paper is to construct a fractal with the help of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the setup of b-metric space. Consequently, we obtain a variety of results for iterated function system satisfying a different set of contractive conditions. Our results unify, generalize, and extend various results in the existing literature.

  • 15.
    Qi, Xiaomin
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Silvestrov, Sergei
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Nazir, Talat
    Department of Mathematics, COMSATS Institute of Information Technology.
    Data classification with support vector machine and generalized support vector machine2017Ingår i: AIP Conference Proceedings, Volume 1798 / [ed] Seenith Sivasundaram, 2017, Vol. 1798, s. 020126-1-020126-9, artikel-id 020126Konferensbidrag (Refereegranskat)
    Abstract [en]

    In the paper, we study the theory of support vector machine and the using for linear and nonlinear classification of data. And we also used the notion of generalized support vector machine for data classifications. We show that the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions.

  • 16.
    Silvestrov, Sergei
    et al.
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
    Nazir, Talat
    Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. Department of Mathematics, COMSATS Institute of Information Technology.
    Common Fixed Points of Weakly Commuting Multivalued Mappings on a Domain of Sets Endowed with Directed Graph2016Ingår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rančić, Springer, 2016Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    In this paper, the existence of coincidence points and common fixed points for multivalued mappings satisfying certain graphic ψ- contraction contractive conditions with set-valued domain endowed with a graph, without appealing to continuity, is established. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.

1 - 16 av 16
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