Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces

Abstract

The main aim of this paper is to establish some fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces, respectively.

Alternative proofs of some classical metric fixed point theorems by using approximate fixed point sequences

“…4. The technique of proof used in the present paper, essentially based on the concepts of graphic contraction and approximate fixed point sequence, could also be nontrivially applied to other classes of self and nonself single-valued mappings in the literature on metric fixed point theory, see [5,[7][8][9][10][11][12]14,20,23,28,31,36,38,39,42,44,46,50,60,61,63] etc. 5.…”

“…Now, by (iii) we obtain that p ∈ Fi x (T ) and by (iv) that Fi x (T ) = {p}. Remark 3.4 Note that in the case of Ćirić-Reich-Rus contractions, condition (ii) in Theorem 3.3 is not always satisfied, because these mappings are in general not continuous, see the examples in [11].…”

Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators

“…Therefore, by (21), T λ is a Chatterjea contraction. It follows from [20] that T λ satisfies Condition (21) and also satisfies Condition (11), since for the value of λ = 1 b+1 , the inequality (11) is the same as Condition (A). This suggests that T is an enriched quasicontraction.…”

Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps

“…Fixed point theory plays an important role in various branches of mathematics as well as in nonlinear functional analysis, and is very useful for solving many existence problems in nonlinear differential and integral equations with applications in engineering and behavioural sciences. Recently, many authors have provided the extended fixed point theorems for the different classes of contraction type mappings, such as Kannan, Reich, Chatterjea and Ćirić-Reich-Rus mappings (see [1][2][3][4][5][6][7][8][9][10]).…”