References
- K. Fan (1969). Extensions of two mixed point theorems of F. E. Browder. Math. Z. 122:234–240.
- W. Takahashi (2000). Nonlinear Functional Analysis, Mixed Point Theory and Its Applications. Yokahama Publishers, Yokahama, Japan.
- W. Takahashi (2000). Convex Analysis and Approximation of Fixed Points. Yokahama Publishers, Yokahama, Japan.
- A. Anthony Eldred and P. Veeramani (2006). Existence and convergence of best proximity points. J. Math. Anal. Appl. 323:1001–1006.
- L. M. Bregman (1967). The relation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys. 7:200–217.
- G. Chen and M. Teboulle (1993). Convergence analysis of a proximal-like minimization algorithm using Bregman functions. SIAM J. Optimization 3:538–543.
- Y. Censor and A. Lent (1981). An iterative row-action method for interval convex programming. J. Optim. Theory Appl. 34:321–358.
- W. Takahashi, N. -C. Wong, and J. -C. Yao (2012). Fixed point theorems and convergence theorems for generalized nonspreading mappings in Banach spaces. J. Fixed Point Theory and Appl. 11:159–183.
- S. Reich and S. Sabach (2010). Existence and approximation of fixed points of Bregman firmly nonexpansive mappings in reflexive Banach spaces. Fixed-Point Algorithms for Inverse Problems in Science and Engineering. (H. H. Bauschke, R. Burachik, P. L Combettes, V. Elser, D. R. Luke and H. Wolkowicz, Eds.) Springer, New York, pp. 299–314.
- S. Reich and S. Sabach (2010). Two strong convergence theorems for a proximal method in reflexive Banach spaces. Numerical Functional Analysis and Optimization 31:22–44.
- E. Naraghirad, W. Takahashi, and J. -C. Yao (2012). Generalized retraction and fixed point theorems using Bregman functions in Banach spaces. Journal of Nonlinear and Convex Analysis 13(1):141–156.
- E. Naraghirad (2013). Halpern’s iteration for Bregman relatively nonexpansive mappings in Banach spaces. Numerical Functional Analysis and Optimization 34(10):1129–1155.
- M. Dela Sen (2013). On best proximity point theorems and fixed point theorems for cyclic hybrid self-mappings in Banach spaces. Abstract and Applied Analysis Article ID 183174; 14 p.
- H. H. Bauschke, J. Chen, and X. Wang (2015). A Bregman projection method for approximating fixed points of quasi-Bregman nonexpansive mappings. Applicable Analysis 94(1):75–84.
- R. Espínola, G. S. R. Kosuru, and P. Veeramani (2015). Pythagorean property and Best-proximity point theorems. Journal of Optimization Theory and Applications 164:534–550.
- W. A. Kirk, P. S. Srinivasan, and P. Veeramani (2003). Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4:79–89.
- A. Anthony Eldred, V. Sankar Raj, and P. Veeramani (2011). On best proximity pair theorems for relatively u-continuous mappings. Nonlinear Analysis 74:3870–3875.
- S. Reich (1978). Approximate selections, best approximations, fixed points and invariant sets. J. Math. Anal. Appl. 62:104–113.
- V. M. Seghal and S. P. Singh (1988). A generalization of multifunctions of Fans best approximation theorem. Proc. Amer.Math. Soc. 102:534–537.
- J. B. Prolla (2010). Fixed point theorems for set valued mappings and existence of best approximations. Numer. Funct. Anal. Optim. 5:449–455
- D. Butnariu and A. N. Iusem (2000). Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization. Kluwer Academic Publishers, Dordrecht.
- F. Kohsaka and W. Takahashi (2005). Proximal point algorithms with Bregman functions in Banach spaces. Journal of Nonlinear and Convex Analysis 6(3):505–523.
- C. Zǎlinescu (2002). Convex Analysis in General Vector Spaces. World Scientific Publishing Co., Inc., River Edge, New Jersey.
- K. Goebel and W. A. Kirk (1990). Topics in Metric Fixed Point Theory. Cambridge University Press, Cambridge.
- E. Naraghirad and J. -C. Yao (2013). Bregman weak relatively nonexpansive mappings in Banach Spaces. Fixed Point Theory and Applications 141:1–43.
- R. T. Rockafellar (1966). Characterization of subdifferentials of convex functions. Pacific. J. Math. 17:497–510.
- R. T. Rockafellar (1970). On the maximal monotonicity of subdifferential mappings. Pacific J. Math. 33:209–216.
- S. S. Basha, N. Shahzad, and R. Jeyaraj (2013). Best proximity points: approximation and optimization. Optimization Letters 7:145–155.
- Y. Su and J. -C. Yao (2015). Further generalized contraction mapping principle and best proximity theorem in metric spaces. Fixed Point Theory and Applications 120:1–13.