Keywords:-
Article Content:-
Abstract
In this paper, we prove some strong and -convergence results for generalized non-expansive mappings through JF-iterative process in hyperbolic spaces.
References:-
References
Agrawal R P, O’Regan D, Sahu D R(2007) Iterative construction of fixed points of nearly asymptotically non-expansive mappings. J Nonlinear Convex Anal 8(1):61–79.
Ali J, Ali F, Kumar P(2019) Approximation of fixed points for Suzuki’s generalized non-expansive mappings. Mathematics 7(6): 522.
Ali F, Ali J, Nieto J(2020) Some observation on generalized non-expansive mappings with an application. Comput Appl Math39:74.
Bogin J(1976) A generalization of a fixed points theorem of Goebel,Kirk and Shimi.Can Math Bull 19:7-12.
Chuadchawna P, Ali F, Kaewcharoen A(2020) fixed point approximate of generalized non-expansive mapping via generalized-iterative process in hyperbolic spaces. I J Math Sci 6435043: p6s.
Dhomphongsa S, Panyanak B(2008) ∆-Convergence theorem in CAT(0) spaces. Comput Math Appl 56(10) :2572–2579.
Dhomphongsa S, Inthakon W, Kaewkhao A(2009) Edelstein’s method and fixed point theorems for some generalized non-expansive mappings. J Math Anal Appl 350(1):12–17.
Fukhar-ud-din H, Saleh K(2018) One-step iterations for a finite family of generalized non-expansive mappings in CAT(0) spaces. Bull Malays Math Sci Soc 41(2):597–608.
Fuster E L, Gàlvez E M(2011) The fixed point theory for some generalized non-expansive mappings, Abst Appl Anal 2011:p15s.
Goebel K, Kirk W A, Shimi T N(1973) A fixed point theorem in uniformly convex spaces. Boll Un Mat Ital.7:67–75.
Gromov M(2001) Mesoscopic curvature and Hyperbolicity. Cont math 288:58-69
Gursoy F, Karakaya V(2014) A Picard-S hybrid type iteration method for solving a differential equation with retarded argument. arXiv:1403.2546v2.
Gürsoy F(2016) A Picard-S iterative method for approximating fixed point of weak-contraction mappings. Filomat 30(10):2829–2845.
Gürsoy F, Khan A R, Ertürk M, Karakaya V(2018) Convergence and data dependency of normal-S iterative method for discontinuous operators on Banach space. Numer Funct Anal Optim 39(3):322–345.
Gürsoy F, Eksteen J A, Khan A R, Karakaya V(2019) An iterative method and its application to stable inversion. Soft Comput 23(16):7393–7406.
Hardy G F,Rogers T D(1973) A generalization of a fixed-point theorem of Reich.Can Math Bull16:201-206.
Ishikawa S(1974) Fixed points by a new iteration method. Proc Am Math Soc 44:147–150.
Khan R A, Fukhar-ud-din H(2012) An implicit algorithm for two finite families of non-expansive maps in hyperbolic spaces. Fixed point theory A54.
Kohlenbach U(2005), Some logical meta theorems with applications in functional analysis. Trans Ameri Math Soci 357(1):89–129.
Leustean L(2007) A quadratic rate of asymptotic regularity for CAT(0) spaces. J Math Anal Appl 235:386–399.
Leustean L(2010) Non-expansive iteration in uniformly convex -hyperbolic spaces, in Nonlinear Anal Opt I. Nonlinear Anal. Conte Math, Leizarowitz A, Mordukhovich B S, Shafrir I, Zaslavski A, Eds., Ramat Gan Am Math Soci.
Lim T C(1976) Remark on some fixed point theorems. Proc Amer Math Soc 60:179–182.
Mann W R(1953) Mean value methods in iteration. Proc Amer Math Soc 4:506–510.
Markin J(1973), Continuous depence of fixed point sets. Proc Am Math Soci 38:545–547.
Noor M A(2000) New approximation schemes for general variational inequalities.J Math Appl 251(1):217-229.
Picard E(1890) Memoire sur la theorie des equations aux derivees partielles et la methode desapproximations successives. J Math Pures Appl 6:145–21.
Reich S, Shafrir I(1990) Non-expansive iterations in hyperbolic spaces.Nonlinear Anal Theo,Meth Appl 15(6):537–558.
Senter H F, Dotson W G(1974) Approximating fixed points of non-expansive mappings. Proc Am Math Soc 44(2):375–380.
Suzuki T(2008) Fixed point theorems and convergence theorems for some generalized non-expansive mappings. J Math Anal Appl 340(2):1088–1095.
Thakur B S, Thakur D, Postolache M(2016) A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized non-expansive mappings. Appl Math Comput 275:147–155.
Uddin I, Imdad M(2015) Some convergence theorems for a hybrid pair of generalized non-expansive mappings in CAT(0) spaces. J Nonlinear Convex Anal 16(3):447–457.
Uddin I, Imdad M(2015) On certain convergence of S-iteration scheme in CAT(0) spaces. Kuwait J Sci 42(2):93–106.
Uddin I, Imdad M(2018) Convergence of SP-iteration for generalized non-expansive mapping in Hadamard spaces. Hacet J Math Stat 47(6):1595–1604.
Wong C S(1974) Generalized contractions and fixed point theorems. Proc Am Math Soc 42:409–41.