Cite

[1] D.D. Bainov and S.G. Hristova, Differential Equations with Maxima, CRC Press, 201110.1201/b10877Search in Google Scholar

[2] V. Berinde, Approximating fixed points of weak contractions using the Picard iter- ation, Nonlinear Anal. Forum, 9, (2004), 43-53Search in Google Scholar

[3] V. Berinde, Iterative Approximation of Fixed Points, Springer, 200710.1109/SYNASC.2007.49Search in Google Scholar

[4] V. Berinde and M. Choban, Generalized distance and their associate metrics. Impact on fixed point theory, Creative Math. Infor., 22 (1), (2013), 23-3210.37193/CMI.2013.01.05Search in Google Scholar

[5] V. Berinde, Şt. Măruşter, and I.A. Rus, An abstract point of view on iterative approximation of fixed point of nonself operators, J. Nonlinear Convex Anal., 15, (2014), 851-865Search in Google Scholar

[6] V. Berinde, Şt. Măruşter, and I.A. Rus, Some variants of contraction principle for nonself operators, generalizations and applications, (to appear)Search in Google Scholar

[7] V. Berinde and M. Păcurar, Fixed points and continuity of almost contractions, Fixed Point Theory, 9 (1), (2008), 23-34Search in Google Scholar

[8] V. Berinde and M. Păcurar, Iterative approximation of fixed point of single- valued almost contraction, In: M.R. Alfuraidan and Q.H. Ansari (eds.), Fixed Point Theory and Graph Theory, Elsevier, (2016), 29-97Search in Google Scholar

[9] V. Berinde, A. Petruşel, I.A. Rus, and M.A. Şerban, The retraction- displacement condition in the theory of fixed point theory equations with a convergent iterative algorithm, In: T.M. Rassias and V. Gupta (eds.), Mathematical Analysis, Approximation Theory and Their Applications, Springer, (2016), 75-106Search in Google Scholar

[10] V. Berinde and I.A. Rus, Caristi-Browder operator theory in distance spaces, In: M.R. Alfuraidan and Q.H. Ansari (eds.), Fixed Point Theory and Graph Theory, Elsevier, (2016), 1-28Search in Google Scholar

[11] A. Buică, Principii de coincidenţă şi aplicaţii, Presa Univ. Clujeană, Cluj-Napoca, 2001Search in Google Scholar

[12] C.E. Chidume and Şt. Măruşter, Iterative methods for the computation of fixed point of demicontractive mappings, J. Comput. Appl. Math., 234, (2010), 861-88210.1016/j.cam.2010.01.050Search in Google Scholar

[13] L.B.Ćirić, On some maps with a nonunique fixed point, Publ. L'Inst. Math., 17, (1974), 52-58Search in Google Scholar

[14] E. Egri, On First and Second Order Iterative Functional Di_erential Equations and Systems, Ph.D. Dissertation, Babeş-Bolyai Univ., Cluj-Napoca, 2007Search in Google Scholar

[15] A.-D. Filip, Fixed Point Theory in Kasahara Spaces, Casa Cărţii de Ştiinţă, Cluj- Napoca, 2015Search in Google Scholar

[16] A. Granas and J. Dugundji, Fixed Point Theory, Springer, 200310.1007/978-0-387-21593-8Search in Google Scholar

[17] V.A. Ilea, Ecuaţii diferenţiale de ordinul întâi cu modificarea mixtă a argumentului, Presa Univ. Clujeană, Cluj-Napoca, 2006Search in Google Scholar

[18] W.A. Kirk and N. Shahzad, Fixed Point Theory in Distance Spaces, Springer, 201410.1007/978-3-319-10927-5Search in Google Scholar

[19] W.A. Kirk and B. Sims (eds.), Handbook of Metric Fixed Point Theory, Kluwer, 200110.1007/978-94-017-1748-9Search in Google Scholar

[20] N. Lungu, Qualitative Problems in the Theory of Hyperbolic Differential Equations, Digital Data Cluj, Cluj-Napoca, 2006Search in Google Scholar

[21] Şt. Măruşter and I.A. Rus, Kannan contractions and strongly demicontractive mappings, Creative Math. Inform., 24 (2), (2015), 171-18010.37193/CMI.2015.02.10Search in Google Scholar

[22] V. Mureşan, Functional Integral Equations, Mediamira, Cluj-Napoca, 2003Search in Google Scholar

[23] I.M. Olaru, A study of a nonlinear integral equation via weakly Picard operators, Fixed Point Theory, 16 (1), (2015), 163-174Search in Google Scholar

[24] J.M. Ortega and W.C. Rheinboldt, Iterative Solutions of Nonlinear Equations in Several Variables, Acad. Press, New York, 1970Search in Google Scholar

[25] M.O. Osilike, Stable iteration procedures for strong pseudo-contractions and non- linear operators, J. Math. Anal. Appl., 204, (1996), 677-69210.1006/jmaa.1996.0461Search in Google Scholar

[26] D. Otrocol, Sisteme Lotka-Volterra cu argument întâirziat, Presa Univ. Clujeană, Cluj-Napoca, 2007Search in Google Scholar

[27] B.G. Pachpatte, On Ćirić type maps with a nonunique fixed point, Indian J. Pure Appl. Math., 10, (1979), 1039-1043Search in Google Scholar

[28] M. Păcurar, Iterative Methods for Fixed Point Approximation, Risoprint, Cluj- Napoca, 2009Search in Google Scholar

[29] M. Păcurar and I.A. Rus, Fixed point theory for cyclic '-contractions, Nonlinear Anal., 72, (2010), 1181-118710.1016/j.na.2009.08.002Search in Google Scholar

[30] A. Petruşel, Multivalued weakly Picard operators and applications, Sci. Math. Jpn., 59, (2004), 167-202Search in Google Scholar

[31] A. Petruşel, Some variants of contraction principle for multivalued operators, generalizations and applications, (to appear)Search in Google Scholar

[32] A. Petruşel and I.A. Rus, An abstract point of view on iterative approximation schemes of fixed point for multivalued operators, J. Nonlinear Sci. Appl., 6, (2013), 97-10710.22436/jnsa.006.02.05Search in Google Scholar

[33] A. Petruşel, I.A. Rus, and M.A. Şerban, The role of equivalent metrics in fixed point theory, Topological Methods in Nonlinear Anal., 41 (1), (2013), 85-11210.1186/1687-1812-2013-218Search in Google Scholar

[34] A. Petruşel, I.A. Rus, and M.A. Şerban, Basic problems of the metric fixed point theorem for a multivalued operator, J. Nonlinear and Convex Anal., 15 (3), (2014), 493-513Search in Google Scholar

[35] R. Precup, The role of the matrices that are convergent to zero in the study of semilinear operator systems, Math. Computer Modeling, 49, (2009), 703-70810.1016/j.mcm.2008.04.006Search in Google Scholar

[36] P.D. Proinov, A unified theory of cone metric spaces and its applications to the fixed point theory, Fixed Point Theory Appl. 2013; 2013:103Search in Google Scholar

[37] I.A. Rus, Generalized Contractions and Applications, Cluj Univ. Press, Cluj-Napoca, 2001Search in Google Scholar

[38] I.A. Rus, Picard operators and applications, Sci. Math. Jpn., 58, (2003), 191-219Search in Google Scholar

[39] I.A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevance, Fixed Point Theory, 9 (2), (2008), 541-559Search in Google Scholar

[40] I.A. Rus, Gronwall lemmas: ten open problems, Sci. Math. Jpn., 70, (2009), 221-228Search in Google Scholar

[41] I.A. Rus, Some nonlinear functional differential and integral equations, via weakly Picard operator theory: a survey, Carpathian J. Math., 26 (2), (2010), 230-258Search in Google Scholar

[42] I.A. Rus, An abstract point of view on iterative approximation of fixed points: impact on the theory of fixed point equations, Fixed Point Theory, 13 (1), (2012), 179-192Search in Google Scholar

[43] I.A. Rus, Results and problems in Ulam stability of operatorial equations and in- clussions, In: T.M. Rassias (ed.), Handbook of Functional Equations: Stability Theory, Springer, (2014), 323-352Search in Google Scholar

[44] I.A. Rus, Some variants of contraction principle, generalizations and applications, Studia Univ. Babeş-Bolyai Math. (to appear)Search in Google Scholar

[45] I.A. Rus, A.S. Mureşan, and V Mureşan, Weakly Picard operators on a set with two metrics, Fixed Point Theory, 6 (2), (2005), 323-331Search in Google Scholar

[46] I.A. Rus, A. Petruşel, and G. Petruşel, Fixed Point Theory, Cluj Univ. Press, Cluj-Napoca, 2008Search in Google Scholar

[47] I.A. Rus, A. Petruşel, and M.A. Şerban, Weakly Picard operators: equivalent definitions, applications and open problems, Fixed Point Theory, 7 (1), (2006), 3-22Search in Google Scholar

[48] I.A. Rus and M.A. Şerban, Basic problems of the metric fixed point theory and the relevance of a metric fixed point theorem, Carpathian J. Math., 29 (2), (2013), 239-25810.37193/CJM.2013.02.04Search in Google Scholar

[49] M.A. Şerban, Teoria punctului fix pentru operatori definiţi pe produs cartezian, Presa Univ. Clujeană, Cluj-Napoca, 2002Search in Google Scholar

[50] M.A. Şerban, Fiber contraction principle, generalizations and applications, (to ap- pear)Search in Google Scholar

[51] M. Turinici, Selected Topics in Metrical Fixed Point Theory, Editura Pin, 2014Search in Google Scholar

[52] J. Wang, J. Deng, and W. Wei, Fractional iterative functional differential equations with impulses, Fixed Point Theory, 17 (1), (2016), 189-200Search in Google Scholar

[53] J. Wang, Y. Zhou, and M. Medved, Picard and weakly Picard operators techniques for nonlinear differential equations in Banach spaces, J. Math. Anal. Appl., 389 (1), (2012), 261-27410.1016/j.jmaa.2011.11.059Search in Google Scholar

[54] D.Y. Zhou, Basic Theory of Fractional Differential Equations, World Sci. Publ. Co, 2014 10.1142/9069Search in Google Scholar

eISSN:
1841-3307
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Mathematics, General Mathematics