Some coincidence and common fixed point theorems for ordered Prešić-Reich type contractions

Abstract

The purpose of this paper is to prove some coincidence and common fixed point theorems for ordered Prešić-Reich type contractions in ordered metric spaces. Results of this paper generalize and extend several known results from metric spaces into product spaces when the underlying space is an ordered metric space. An example illustrates the case when new results can be applied while old ones cannot.

Iterative approximation of fixed points of generalized weak Presic type k-step iterative method for a class of operators

“…, x k ∈ X, the sequence {x n } defined by (1.1) converges to x * . For other results on Prešić operators, we refer to [3,4,6,8,13,16,17,[20][21][22][23][24]. In this paper, we study the convergence of the sequence {x n } defined by (1.1) for the mapping f : X k → X satisfies various contractive conditions of Prešić type.…”

Fixed Point Results for Multivalued Prešić Type Weakly Contractive Mappings

“…Various other useful results of generalized Prešić type operators and its applications in various spaces are presented in [11,[13][14][15][16][17][18][19][20]. Recently, Alecsa [21] introduced Prešić convex contraction and obtained the unique fixed point in the setup of metric spaces.…”

“…Recently, Shulka et al [20] introduced the notion of set-valued Prešić type contraction mapping in product spaces. Definition 2.…”

On (G, G′)-Prešić–Ćirić Operators in Graphical Metric Spaces

“…Prešić type operators have several applications to solve problems in applied mathematics-see, for example, [6,7,[9][10][11][12][13][14]. Recently, many authors worked on the result of Prešić in various directions-see [8,[15][16][17][18][19][20][21][22][23]. Ran and Reurings [2] and Nieto and Lopez [24,25] gave fixed point results in metric spaces via a partial order.…”