In this paper, we study the convergence of new implicit iterations dealing with n-tupled fixed po... more In this paper, we study the convergence of new implicit iterations dealing with n-tupled fixed point results for nonlinear contractive-like mappings on W-hyperbolic metric spaces. Herein, we demonstrate that our newly implicit iteration schemes have faster rate of convergence than implicit S-iteration process, implicit Ishikawa and Mann type iteration processes. Furthermore, a numerical simulation to improve our theoretical results is obtained.
The aim of this note is to point out a fallacy in the proof of Theorem 3.1 contained in the recen... more The aim of this note is to point out a fallacy in the proof of Theorem 3.1 contained in the recent paper ( Int. J. Contemp. Math. Sci. 5 (2010), 2699-2707) proved in intuitionistic fuzzy metric spaces employing the newly introduced notion of sub-compatible pair of mappings wherein our claim is also substantiated with the aid of an appropriate example. We also rectify the erratic theorem in two ways. In order to avoid repetition and also due to paucity of the space, we assume the terminology and the notations utilized in [6] rather than presenting the same again. For more recent developments, we refer the readers to [1, 3, 9] and references cited therein. The following definitions are essentially contained in [6]. Definition 0.1. Let (X,M,N, ∗, ⋄) be an intuitionistic fuzzy metric space. A pair of self maps (A,S) defined on X is said to be compatible iff lim n→∞ M(ASxn, SAxn, t) = 1 and lim n→∞ N(ASxn, SAxn, t) = 0 wherein {xn} are sequences in X with lim n→∞ Axn = lim n→∞ Sxn = z, z...
In this note, we present a sharpened form of a recent general even-tupled coincidence theorem due... more In this note, we present a sharpened form of a recent general even-tupled coincidence theorem due to Imdad et al: (Journal of Operators, Volume 2013 (2013) Art. ID 532867, 8 pp.) and also furnish a proof which also oers consolidation to the proof of the theorem of Imdad et al. which contains some gaps. Unfortunately, certain earlier core results on coupled coincidence points due to Lakshmikantham and Ciric (Nonlinear Anal. 70 (2009), 4341-4349) and quadruple coincidence points due to Karapinar and Berinde (Banach J. Math. Anal. 6 (1) (2012), 74-89) also contain some errors. Besides consolidating the proofs of earlier mentioned results, we also prove a corresponding unique common even tupled fixed point theorem. Finally, we demonstrate that such theorems can not be extended to odd natural numbers besides furnishing an illustrative example for our results.
A common fixed point theorem for eight noncontinuous pairwise coincidentally commuting mappings f... more A common fixed point theorem for eight noncontinuous pairwise coincidentally commuting mappings for Delbosco type contractions is proved which generalizes relevant known results due to Delbosco, Fisher-Sessa, Fisher, Kannan and others. Some related results and illustrative examples are also discussed.
Bulletin of Mathematical Sciences and Applications, 2014
In this paper, we establish a common fixed point theorem in semi-metric space with compatible map... more In this paper, we establish a common fixed point theorem in semi-metric space with compatible mapping of type (E) which improves and extends similar known results in the literature.
... A special form of Rund's h-curvature tensor using $R3$-like Finsler space. ST Aveesh... more ... A special form of Rund's h-curvature tensor using $R3$-like Finsler space. ST Aveesh, Pradeep Kumar, HG Nagaraja and SK Narasimhamurthy; 175-180. ...
The concept of compositely asymptotically regular maps is introduced and used to prove common fix... more The concept of compositely asymptotically regular maps is introduced and used to prove common fixed point theorems on complete metric spaces. Our work generalizes some earlier results of Nesic, Guay and Singh, Sharma and Yuel and others.
In this paper, we study the convergence of new implicit iterations dealing with n-tupled fixed po... more In this paper, we study the convergence of new implicit iterations dealing with n-tupled fixed point results for nonlinear contractive-like mappings on W-hyperbolic metric spaces. Herein, we demonstrate that our newly implicit iteration schemes have faster rate of convergence than implicit S-iteration process, implicit Ishikawa and Mann type iteration processes. Furthermore, a numerical simulation to improve our theoretical results is obtained.
The aim of this note is to point out a fallacy in the proof of Theorem 3.1 contained in the recen... more The aim of this note is to point out a fallacy in the proof of Theorem 3.1 contained in the recent paper ( Int. J. Contemp. Math. Sci. 5 (2010), 2699-2707) proved in intuitionistic fuzzy metric spaces employing the newly introduced notion of sub-compatible pair of mappings wherein our claim is also substantiated with the aid of an appropriate example. We also rectify the erratic theorem in two ways. In order to avoid repetition and also due to paucity of the space, we assume the terminology and the notations utilized in [6] rather than presenting the same again. For more recent developments, we refer the readers to [1, 3, 9] and references cited therein. The following definitions are essentially contained in [6]. Definition 0.1. Let (X,M,N, ∗, ⋄) be an intuitionistic fuzzy metric space. A pair of self maps (A,S) defined on X is said to be compatible iff lim n→∞ M(ASxn, SAxn, t) = 1 and lim n→∞ N(ASxn, SAxn, t) = 0 wherein {xn} are sequences in X with lim n→∞ Axn = lim n→∞ Sxn = z, z...
In this note, we present a sharpened form of a recent general even-tupled coincidence theorem due... more In this note, we present a sharpened form of a recent general even-tupled coincidence theorem due to Imdad et al: (Journal of Operators, Volume 2013 (2013) Art. ID 532867, 8 pp.) and also furnish a proof which also oers consolidation to the proof of the theorem of Imdad et al. which contains some gaps. Unfortunately, certain earlier core results on coupled coincidence points due to Lakshmikantham and Ciric (Nonlinear Anal. 70 (2009), 4341-4349) and quadruple coincidence points due to Karapinar and Berinde (Banach J. Math. Anal. 6 (1) (2012), 74-89) also contain some errors. Besides consolidating the proofs of earlier mentioned results, we also prove a corresponding unique common even tupled fixed point theorem. Finally, we demonstrate that such theorems can not be extended to odd natural numbers besides furnishing an illustrative example for our results.
A common fixed point theorem for eight noncontinuous pairwise coincidentally commuting mappings f... more A common fixed point theorem for eight noncontinuous pairwise coincidentally commuting mappings for Delbosco type contractions is proved which generalizes relevant known results due to Delbosco, Fisher-Sessa, Fisher, Kannan and others. Some related results and illustrative examples are also discussed.
Bulletin of Mathematical Sciences and Applications, 2014
In this paper, we establish a common fixed point theorem in semi-metric space with compatible map... more In this paper, we establish a common fixed point theorem in semi-metric space with compatible mapping of type (E) which improves and extends similar known results in the literature.
... A special form of Rund's h-curvature tensor using $R3$-like Finsler space. ST Aveesh... more ... A special form of Rund's h-curvature tensor using $R3$-like Finsler space. ST Aveesh, Pradeep Kumar, HG Nagaraja and SK Narasimhamurthy; 175-180. ...
The concept of compositely asymptotically regular maps is introduced and used to prove common fix... more The concept of compositely asymptotically regular maps is introduced and used to prove common fixed point theorems on complete metric spaces. Our work generalizes some earlier results of Nesic, Guay and Singh, Sharma and Yuel and others.
Uploads
Papers by M. Imdad