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In the paper of the author [M. O. Olatinwo; Stability and convergence results for Das-Debata type iterative process using simultaneous set of contractive conditions of integral type, Bulletin of the Allahabad Mathematical Society 30 (1) (2015), 75-94], the Jungck-Das-Debata iterative process involving the nonself-mappings R, S and T was introduced. The (R, S, T)-stability of iterative processes was then initiated in the same article. The convergence result was also proved for the Jungck-Das-Debata iterative process. In the present article, we shall obtain some stability and strong convergence results for the iterative processes of Agarwal-O'Regan-Sahu, Jungck-Das-Debata and a new Jungck-Ishikawa type iteration for a new class of contractive conditions. Our results generalize and extend amongst others the stability results of [S. L. Singh, C. Bhatnagar, S. N. Mishra; Stability of Jungck-type iterative procedures, Int. J. Math. & Math. Sc. 19 (2005), 3035-3043] as well as stability and convergence results contained in [V. Berinde; Iterative approximation of fixed points, Springer-Verlag, Berlin Heidelberg (2007)] and a host of others in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some unifying fixed point theorems of Ćirić's type in a complete b-metric space for mappings possessing non-unique fixed points by employing general contractive inequality conditions as well as the notion of comparison functions. The right-hand side of each of the contractive inequality condition being introduced is Akram-Zafar-Siddiqui while the left-hand side of each is Akram-Zafar-Siddiqui type to certain extent. Our results unify, generalize and improve several unique and non-unique fixed point theorems in the literature. Also, the results obtained are extensions of such unique and non-unique fixed point theorems from the metric space setting to the b-metric space environment. [ABSTRACT FROM AUTHOR]

In this paper, some coupled fixed point stability results for one and two metrics are obtained in complete metric spaces by using some general contractive conditions some of which involve comparison functions. Our results are generalizations and exten- sions of [M.O. Olatinwo: Some stability results in complete metric space, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 48(2009), 83-92] and [M.O. Olatinwo: Stability of coupled fixed point iterations and the continuous dependence of coupled fixed points, Comm. Appl. Nonlinear Anal., 19(2012), No. 2, 71-83] as well as some others in the literature. [ABSTRACT FROM AUTHOR]

Let (X, d) be a complete metric space and T: X→X a mapping of X. In 1975 Dass and Gupta introduced the following rational type contractive condition to prove a generalization of Banach's Fixed Point Theorem: For α, β∈ [0, 1), such that α + β < 1, we have ∀x, y ∈ X, d(Tx, Ty) ≤ α d(y, Ty)(1 +d(x, Tx)) / 1 + d(x, y) + βd(x, y), where T is continuous. There are several generalization and extension of Dass and Gupta’s result under the hypothesis that T is continuous and α + β < 1. In this paper, we prove some fixed point theorems in a complete metric space setting by employing more general rational type contractive conditions than the above one. We show in our results that the continuity of the above operator T is unnecessary and the restrictive condition that α + β < 1 is also removed. Our results generalize and extend those of Das and Gupta and several known results in the literature. [ABSTRACT FROM AUTHOR]

Recently, in the papers [14] and [15], the author established some results pertaining to the continuous dependence of the fixed points in normed space and Banach space settings for some iterative processes by using general contractive conditions. Both papers were devoted to the partial fulfillment of the open question in [3], that is, "apart from the Picard iteration, the continuous dependence of the fixed points has not been studied so far for other fixed point iteration procedures." In the present paper, our purpose is to further investigate the continuous dependence of the fixed points in uniformly convex Banach space for nonexpansive and quasi-nonexpansive mappings. Our results extend some recently announced ones in the current literature. [ABSTRACT FROM AUTHOR]

In the present paper, the notion of stability of fixed point iterative procedure of [A.M. Harder and T.L. Hicks: Stability results for fixed point iteration procedures, Math. Japonica, 33(1988), No. 5, 693-706] is extended from the fixed point setting to the approximate fixed point and approximate coincidence point considerations. These extensions are possible by introducing new notions of stability of iterative procedures; viz- (ε; T)-stability and (ε; S; T)-stability. The notion of approximate coincidence point was initiated in the article [M.O. Olatinwo: Some approximate fixed point and approximate coincidence point theorems in b-metric spaces, J. Adv. Math. Stud., 11(2018), No. 3, 576-586], and the notion in this article is employed in this present article. Some strong convergence results pertaining to some celebrated fixed point iterative procedures are also extended from the fixed point setting to the approximate fixed point (ε-fixed point) and approximate coincidence point (ε-coincidence point) situations. We obtain our results by employing two contractive inequality conditions. Our results generalize and extend a multitude of results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some coupled fixed point theorems in cone metric spaces by assuming that the cone has nonempty interior as well as employing an hybrid contractive-type condition. Our theorems generalize, extend and improve some recently announced results in the literature. In particular, our results extend the recent results of Akram et al from fixed point setting (A-contractions) to the corresponding notion of coupled fixed points (G-contractions). [ABSTRACT FROM AUTHOR]

In the article [R.U. Verma: A fixed-point theorem involving Lipschitzian generalized pseudo-contractions, Math. Proc. R. Ir. Acad., 97A(1997), No. 1, 83-86], the convergence of generalized pseudo-contractive operators were studied with regard to a unique fixed point. In the present paper, we introduce Jungck generalized pseudo-contractive and Lipschitzian type operators in the Hilbert space settings to establish the existence and the uniqueness of a common fixed point of two operators using a novel Jungck-Schaefer's fixed point iterative algorithm. The strong convergence of this new fixed point iterative algorithm to a unique common fixed point is also investigated. In addition, we consider Jungck-Kirk-Mann iterative algorithm to approximate a unique common fixed point of more general type of operators. Example 2.6 and Example 2.7 are given to validate the new type of operators. Our results are new and original as well as generalizing some existing ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish some strong convergence results for the recently introduced Jungck-Mann iteration process of Singh et al. [18] and the newly introduced Jungck-Ishikawa iteration process in the class of non-selfmappings in an arbitrary Banach space. Our results are generalizations and extensions of those of Berinde [4], Rhoades [13, 14] as well as some other analogous ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for new classes of contractive mappings which are generalizations of the A-contractions of Akram et al. Indeed, our results improve, generalize and extend the results of Fisher, Jungck and the recent results of Akram et al. In actual fact, our results unify several other classical results in the literature concerning the fixed point and the common fixed point settings. [ABSTRACT FROM AUTHOR]

In this paper, for certain general contractive conditions, we establish that a self-mapping T has approximate fixed point property and hence, show that the fixed point set of T is nonempty. In addition, we obtain some unifying approximate fixed point theorems as well as approximate coincidence point theorems in b-metric space for mappings satisfying some contractive conditions. Moreover, to the best of our knowledge, the concept of approximate coincidence point is being initiated in the present paper. Our results do not only unify, but also generalize and improve the results of [B. Prasad, B. Singh and R. Sahni: Some approximate fixed point theorems, Int. J. Math. Anal., 3(2009), No. 5, 203-210]. The results of Prasad et al. also extend the corresponding results of [M. Berinde: Approximate fixed point theorems, Stud. Univ. "Babeş Bolyai" Mathematica, 51(2006), No. 1, 11-25] from the metric space to the b-metric space setting. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems which are variants of Achari and Ćirić-Jotić types for mappings having non-unique fixed points by employing some hybrid contractive conditions. Our results generalize, extend and improve some previous and corresponding ones in the literature. [ABSTRACT FROM AUTHOR]