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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.

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.

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.

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.

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.

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.

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.