Fixed point results for materials research

Abstract In this paper, we establish a new Class category of non expansive mappings in metric space which is wider than the class category of mappings satisfying contractive condition (CC). Special properties and various fixed point results for these mappings in metric space are obtained here. Also we discussed the results and examples of the convergence of some iteration schemes to the fixed point in metric space. Obtained results are useful in material research as well as in image processing.

[1]  Fixed Point Theorems and Approximating Fixed Points of Generalized (C)-Condition Mappings , 2013 .

[2]  I. Ramabhadra Sarma,et al.  Metrization theorem for a weaker class of uniformities , 2016 .

[3]  Tomonari Suzuki,et al.  Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces , 2005 .

[4]  C. Vetro,et al.  Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation , 2016 .

[5]  Mujahid Abbas,et al.  Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation , 2014, Appl. Math. Comput..

[6]  Stojan Radenović,et al.  Computational fixed points in graphical rectangular metric spaces with application , 2020, J. Comput. Appl. Math..

[7]  R. Rodríguez-López,et al.  Fuzzy-Prešic-Ciric Operators and Applications to Certain Nonlinear Differential Equations , 2016 .

[8]  T. Abdeljawad,et al.  Novel fixed point approach to Atangana-Baleanu fractional and Lp-Fredholm integral equations , 2020 .

[9]  Some Results on Fixed Point Theorems in Banach Algebras , 2016 .

[10]  Sompong Dhompongsa,et al.  Edelstein's method and fixed point theorems for some generalized nonexpansive mappings , 2009 .

[11]  I. A. Khan,et al.  Common Fixed Point Theorems in Metric Space by Altering Distance Function , 2017 .

[12]  Fatemeh Lael,et al.  Fixed point theorems for a class of generalized nonexpansive mappings , 2016, Fixed Point Theory and Applications.

[13]  Ravi P. Agarwal,et al.  A New Approach to the Solution of Non-Linear Integral Equations via Various FBe-Contractions , 2019, Symmetry.

[14]  Common Fixed Point Theorem in T0 Quasi Metric Space , 2017 .

[15]  Hari M. Srivastava,et al.  Linear operators associated with k-uniformly convex functions , 2000 .

[16]  Erdal Karapinar,et al.  Generalized (C)-conditions and related fixed point theorems , 2011, Comput. Math. Appl..

[17]  K. Nisar,et al.  On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions , 2020 .

[18]  Convergence theorems for generalized nonexpansive mappings in uniformly convex Banach spaces , 2015 .

[19]  V. Mishra,et al.  Dislocated Soft Metric Space with Soft Fixed Point Theorems , 2017 .

[20]  S. S. Chauhan,et al.  A common fixed point theorem in fuzzy 2-metric space , 2013 .

[21]  T. D. Benavides,et al.  The fixed point property for some generalized nonexpansive mappings and renormings , 2015 .

[22]  P. Kumari,et al.  Connecting various types of cyclic contractions and contractive self-mappings with Hardy-Rogers self-mappings , 2016, Fixed Point Theory and Applications.

[23]  S. K. Panda.  Applying fixed point methods and fractional operators in the modelling of novel coronavirus 2019-nCoV/SARS-CoV-2 , 2020, Results in Physics.

[24]  A Common Fixed Point Theorem in Dislocated Metric Space , 2012 .

[25]  Fixed point of α-ψ-contractive type mappings in uniform spaces , 2014 .

[26]  Abdon Atangana,et al.  A numerical schemes and comparisons for fixed point results with applications to the solutions of Volterra integral equations indislocatedextendedb-metricspace , 2020 .

[27]  M. Khamsi,et al.  On monotone nonexpansive mappings in L1([0,1])$L_{1}([0,1])$ , 2015 .

[28]  Enrique Llorens-Fuster,et al.  Fixed point theory for a class of generalized nonexpansive mappings , 2011 .

[29]  Wutiphol Sintunavarat,et al.  New fixed point results for mappings of contractive type with an application to nonlinear fractional differential equations , 2016 .

[31]  V. Mishra,et al.  Some results on fixed point theory for a class of generalized nonexpansive mappings , 2018, Fixed Point Theory and Applications.

[32]  B. Singh,et al.  Some Fixed Point Theorems in Dislocated Metric Space , 2017 .

[33]  E. Karapınar.  Remarks on Suzuki (C)-Condition , 2012 .

[34]  Coupled Fixed Point Theorem in Partially Ordered Metric Spaces , 2013 .

[35]  V. Lakshmikantham,et al.  Fixed point theorems in partially ordered metric spaces and applications , 2006 .

[36]  Erdal Karapinar,et al.  Solutions of the Nonlinear Integral Equation and Fractional Differential Equation Using the Technique of a Fixed Point with a Numerical Experiment in Extended b-Metric Space , 2019, Symmetry.

[37]  E. Karapınar,et al.  Solutions of boundary value problems on extended-Branciari b-distance , 2020 .

[38]  P. Kumam,et al.  Best Proximity point for Z-contraction and Suzuki type Z-contraction mappings with an application to fractional calculus , 2016 .

[39]  Tomonari Suzuki,et al.  FIXED POINT THEOREMS AND CONVERGENCE THEOREMS FOR SOME GENERALIZED NONEXPANSIVE MAPPINGS , 2008 .

[40]  B. Singh,et al.  Coupled fixed point theorems with monotone property in soft b-metric space , 2017 .