n-tuplet fixed point theorems for contractive type mappings in partially ordered metric spaces

Abstract

In this paper, we study existence and uniquennes of fixed points of operator F : X n → X where n is an arbitrary positive integer and X is partially ordered complete metric space.

Unified multi-tupled fixed point theorems involving mixed monotone property in ordered metric spaces

“…As a continuation of this trends, various authors extended the notion of coupled fixed (coincidence) point and mixed monotone (g-monotone) property for the mapping F : X n → X, n ≥ 3 in different ways. A natural extension of mixed monotone property introduced by Berinde and Borcut [19] (for n = 3), Karapinar and Luong [20] (for n = 4), Imdad et al [21] (for even n) and Gordji and Ramezani [22] and Ertürk and Karakaya [23,24] (for general n) runs as follows: Definition 6 ([19]- [23]). Let (X, ) be an ordered set and F : X n → X a mapping.…”

“…• n-tuplet fixed point (see Ertürk and Karakaya[23,24]) • n-fixed point (seeGordji and Ramezani [22], Paknazar et al[28])…”

n-Tuplet Coincidence Point Theorems in Intuitionistic Fuzzy Normed Spaces

“…By inspiring these works, coupled fixed point theorems have been studied for different type contraction mappings (see [5][6][7][8][9][10][11][12]). The interest on coupled fixed point theorem has motivated the authors to generalize it as tripled fixed point theorem in [13,14], afterwards as quadruple fixed point theorem in [15][16][17], and as -tuplet fixed point theorem in [18][19][20][21].…”

n-Tuplet Coincidence Point Theorems in Partially Ordered Probabilistic Metric Spaces

“…Then, some coupled and tripled fixed point results were obtained by many authors [13][14][15][16][17][18][19]. In 2013, Ertürk and Karakaya gave the concept oftuplet fixed point theorems in partially ordered metric spaces [20]. Alam, Imdad, and Ali unified -tuplet fixed point results in ordered metric space in 2016 [21].…”