Fixed Point Theorems for Manageable Contractions with Application to Integral Equations

Abstract

In this paper we utilize the concept of manageable functions to define multivalued α⁎-η⁎ manageable contractions and prove fixed point theorems for such contractions. As applications we deduce certain fixed point theorems which generalize and improve Nadler’s fixed point theorem, Mizoguchi-Takahashi’s fixed point theorem, and some other well-known results in the literature. Also, we give an illustrating example showing that our results are a proper generalization of Nadler’s theorem and provide an application to integral equations.

Common fixed point results of generalized almost rational contraction mappings with an application

“…Following this trend, Samet et al [34] first introduced α-admissible mappings and then α-ψ-contractive type mappings to obtain some interesting generalizations of Banach contraction principle. For more results in this direction, we refer to [6,13,14,16,17,20,21,22,24,28,30,32] and references mentioned therein. Recently, Alizadeh et al [5] defined the concept of cyclic (α, β)-admissible mapping as follows: Definition 1.1 ( [5]).…”

On Convex F-Contraction in b-Metric Spaces

“…Since then, several authors proved fixed point results for F-contractions (see [2][3][4][5][6][7][8][9][10][11][12][13]). However, F-contraction has a great limitation since the mapping must be a continuous mapping (see Remark 2).…”

Fixed Point Results on Closed Ball in Convex Rectangularb−Metric Spaces and Applications

“…Later in 1968, Kannan [2] studied a new type of contractive mapping. Since then, there have been many results related to mappings satisfy various types of contractive inequality, see for example [3][4][5][6][7][8][9].…”