Abstract Recently, Karapinar, Aydi and De Hierro introduced the notions of interpolative Kannan-type contractions CRR-type proved that they possess a fixed point when space is complete. In this paper, we show existence points for remains true metric which not necessarily complete give more precise result concerning behaviour Picard sequences arbitrary initial point. We also study some particula...

Vumile represents an individual with social phobia who experienced a successful outcome after being treated with a manualized treatment based on Clark and Wells’ (1995) theoretical model (Edwards & Kannan, 2006). This commentary reviews issues in the debate regarding manualized treatments, with an emphasis on how the case of Vumile represents the best of what manualized treatments and empirical...

In this paper, we shall establish two fixed point theorems by following the concept of [9, 21] and using weak contractions of the integral type. Our results are generalizations of the classical Banach’s fixed point theorem [1, 2, 3, 4, 5, 7, 25] as well as extensions of some other results of Berinde [4, 5, 6, 7], Berinde and Berinde [8], Branciari [9], Chatterjea [10], Kannan [16] and Zamfiresc...

Bryn Bell, Srikanth Kannan, Alex McMillan, Alex S. Clark, William J. Wadsworth, and John G. Rarity1,∗ Centre for Quantum Photonics, Department of Electrical and Electronic Engineering, University of Bristol, Bristol BS8 1UB, UK Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), Institute of Photonics and Optical Science, University of Sydney, NSW 2006, Australia and Centre for ...

Recently, the fixed-circle problems have been studied with different approaches as an interesting and geometric generalization. In this paper, we present some solutions to open problem CC: what is (are) condition(s) make any circle C?0,? common fixed for two (or more than two) self-mappings? To do this, modify known contractions which are used in fixed-point theorems such Hardy–Rogers-type cont...

K. Griffin Roberts,1 M. Varela,2 S. Rashkeev,3,2,* S. T. Pantelides,3,2 S. J. Pennycook,2,3 and Kannan M. Krishnan1,† 1Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195, USA 2Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 3Department of Physics and Astronomy, Vanderbilt University, Nash...

In this paper, we shall introduce a Jungck-Noor three-step iteration process to establish a strong convergence result for a pair of nonselfmappings in an arbitrary Banach space by employing a general contractive condition. Our result is a generalization and extension of a multitude of results. In particular, it is a generalization and extension of some of the results of Kannan [11, 12], Rhoades...

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to...