Tripled Fixed Point Theorem for Hybrid Pair of Mappings Under Generalized Nonlinear Contraction

Abstract

Abstract. In this paper, we introduce the concept of w−compatibility and weakly commutativity for hybrid pair of mappings F : X × X × X → 2 X and g : X → X and establish a common tripled fixed point theorem under generalized nonlinear contraction. An example is also given to validate our result. We improve, extend and generalize various known results.

Common Tripled Fixed Point Theorems Under Weaker Conditions

“…Remark 1. We improve, extend and generalize the result of Bhaskar and Lakshmikantham [5], Lakshmikantham and Ciric [14] and Luong and Thuan [16] in the following sense:…”

“…Tripled fixed point theory for multivalued mappings was introduced by Deshpande, Sharma and Handa [16] and obtained tripled coincidence points and common tripled fixed point theorems involving hybrid pair of mappings under generalized nonlinear contraction. Very few papers were devoted to coupled and tripled fixed point problems for hybrid pair of mappings including [2,16,17,22].…”

“…In [16], Deshpande, Sharma and Handa introduced the following for multivalued mappings: Definition 1. Let X be a nonempty set F : X × X × X → 2 X (a collection of all nonempty subsets of X) and g be a self-mapping on X.…”

Tripled Coincidence and Common Tripled Fixed Point Theorem for Hybrid Pair of Mappings Satisfying New Contractive Condition

“…Very few researchers focused on tripled fixed point theorems for hybrid pair of mappings including [1,2,3,16,17,18,19,20,21,22,23,24,28,35].…”

Common Coupled Fixed Point for Hybrid Pair of Mappings Under Generalized Nonlinear Contraction

“…The existence of fixed points for various multivalued contractive mappings has been studied by many authors under different conditions. For details, we refer the reader to ( [2], [7], [8], [9], [10], [11], [13], [14], [15], [16], [21], [25], [26], [27]) and the reference therein. The theory of multivalued mappings has applications in control theory, convex optimization, differential inclusions and economics.…”