New Nonlinear Conditions and Inequalities for the Existence of Coincidence Points and Fixed Points

New Nonlinear Conditions and Inequalities for the Existence of Coincidence Points and Fixed Points

Let us begin with some basic definitions and notation that will be needed in this paper. Throughout this paper, we denote by N and R, the sets of positive integers and real numbers, respectively. Let X, d be a metric space. For each x ∈ X, and A ⊆ X, let d x,A infy∈Ad x, y . Denote by N X the class of all nonempty subsets of X, C X the family of all nonempty closed subsets ofX, and CB X the fam...

EXISTENCE OF FIXED POINTS OF CERTAIN CLASSES OF NONLINEAR MAPPINGS

In this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $Phi$-pseudocontra...

New Existence Results and Generalizations for Coincidence Points and Fixed Points without Global Completeness

and Applied Analysis 3 (w3) for any ε > 0, there exists δ > 0 such that p(z, x) ≤ δ and p(z, y) ≤ δ imply d(x, y) ≤ ε. A function p : X×X → [0,∞) is said to be a τ-function [5, 10, 14, 15, 27–29], first introduced and studied by Lin and Du, if the following conditions hold: (τ1) p(x, z) ≤ p(x, y) + p(y, z) for all x, y, z ∈ X; (τ2) if x ∈ X and {yn} in X with limn→∞yn = y such that p(x, yn) ≤ M...

Coincidence Points and Common Fixed Points for Expansive Type Mappings in $b$-Metric Spaces

The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for a pair of self mappings satisfying some expansive type conditions in $b$-metric spaces. Finally, we investigate that the equivalence of one of these results in the context of cone $b$-metric spaces cannot be obtained by the techniques using scalarization function....

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points