Maia type fixed point theorems for some classes of enriched contractive mappings in Banach spaces

Abstract

We give some extensions of the beautiful 1968 fixed point theorem of Maia [Maia, M. G. Un’osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 (1968), 139–143] to three classes of enriched contractive mappings in Banach spaces: enriched contractions, Kannan enriched contractions and Ćirić-Reich-Rus contractions.

Fixed point theorems for $(a,b,\theta)$-enriched contractions

“…They established fixed point theorems, which extended and unified the results presented in [2,16,23]. Further improvements were presented later in [4,5,6,7].…”

“…Due to its importance and applications, the Banach contraction principle has been extensively investigated and generalized by several authors; see, e.g., [3,4,5,6,7,16,18,23]. In 1968, Maia [23] extended the Banach contraction principle in the spaces equipped with two metrics.…”

Common fixed points of generalized F -contraction of multivalued mappings in bi-b-metric spaces

“…In this article, we present an improvement and generalization of the main results in the existing literature (see Maia [20], Iseki [15], Iyer [16], Rus [24] and Khan et al [17], Acar [4], Balazs [7], Berinde [10], Petrusel [22], Sgroi [26], Suzuki [27] and the references therein). Throughout this paper, and denote the set of natural numbers, the set of nonnegative integers, the set of real numbers and the set of positive real numbers, respectively.…”

“…By using two metrics on a set X, Maia [20] extended the conclusions of the wellknown Banach contraction principle. Maia's theorem has been generalized in the past few years, and fixed point theorems have been proved in a variety of approaches by Iseki [15], Iyer [16], Rus [24], Khan et al [17], Berinde [10] and the references therein.…”