Optimality conditions in convex multiobjective SIP

The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk–Kuhn–Tucker multipliers or a new gap function associated with the given problem.This research was partially cosponsored by the Ministry of Economy and Competitiveness (MINECO) of Spain, and by the European Regional Development Fund (ERDF) of the European Commission, Project MTM2014-59179-C2-1-P

Multiple solutions for a class of perturbed second-order differential equations with impulses

n/

Perturbed nonlocal fourth order equations of Kirchhoff type with Navier boundary conditions

Abstract We investigate the existence of multiple solutions for perturbed nonlocal fourth-order equations of Kirchhoff type under Navier boundary conditions. We give some new criteria for guaranteeing that the perturbed fourth-order equations of Kirchhoff type have at least three weak solutions by using a variational method and some critical point theorems due to Ricceri. We extend and improve some recent results. Finally, by presenting two examples, we ensure the applicability of our results

Fixed point theorems for cyclic self-maps involving weaker Meir-Keelerfunctions in complete metric spaces and applications

We obtain fixed point theorems for cyclic self-maps on complete metric spaces involving Meir-Keeler and weaker Meir-Keeler functions, respectively. In this way, we extend several well-known fixed point theorems and, in particular, improve some very recent results on weaker Meir-Keeler functions. Fixed point results for well-posed property and for limit shadowing property are also deduced. Finally, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented.The second author thanks for the support of the Ministry of Economy and Competitiveness of Spain under grant MTM2012-37894-C02-01, and the Universitat Politecnica de Valencia, grant PAID-06-12-SP20120471.Nashine, HK.; Romaguera Bonilla, S. (2013). Fixed point theorems for cyclic self-maps involving weaker Meir-Keelerfunctions in complete metric spaces and applications. Fixed Point Theory and Applications. 2013(224):1-15. https://doi.org/10.1186/1687-1812-2013-224S1152013224Kirk WA, Srinavasan PS, Veeramani P: Fixed points for mapping satisfying cyclical contractive conditions. Fixed Point Theory 2003, 4: 79–89.Banach S: Sur les operations dans les ensembles abstraits et leur application aux equations integerales. Fundam. Math. 1922, 3: 133–181.Boyd DW, Wong SW: On nonlinear contractions. Proc. Am. Math. Soc. 1969, 20: 458–464. 10.1090/S0002-9939-1969-0239559-9Caristi J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 1976, 215: 241–251.Di Bari C, Suzuki T, Vetro C: Best proximity points for cyclic Meir-Keeler contractions. Nonlinear Anal. 2008, 69: 3790–3794. 10.1016/j.na.2007.10.014Karapinar E: Fixed point theory for cyclic weaker ϕ -contraction. Appl. Math. Lett. 2011, 24: 822–825. 10.1016/j.aml.2010.12.016Karapinar E, Sadarangani K: Corrigendum to “Fixed point theory for cyclic weaker ϕ -contraction” [Appl. Math. Lett. Vol. 24(6), 822–825.]. Appl. Math. Lett. 2012, 25: 1582–1584. 10.1016/j.aml.2011.11.001Karapinar E, Sadarangani K:Fixed point theory for cyclic ( ϕ − φ ) -contractions. Fixed Point Theory Appl. 2011., 2011: Article ID 69Nahsine HK: Cyclic generalized ψ -weakly contractive mappings and fixed point results with applications to integral equations. Nonlinear Anal. 2012, 75: 6160–6169. 10.1016/j.na.2012.06.021Păcurar M: Fixed point theory for cyclic Berinde operators. Fixed Point Theory 2011, 12: 419–428.Păcurar M, Rus IA: Fixed point theory for cyclic φ -contractions. Nonlinear Anal. 2010, 72: 2683–2693.Piatek B: On cyclic Meir-Keeler contractions in metric spaces. Nonlinear Anal. 2011, 74: 35–40. 10.1016/j.na.2010.08.010Rus IA: Cyclic representations and fixed points. Ann. “Tiberiu Popoviciu” Sem. Funct. Equ. Approx. Convexity 2005, 3: 171–178.Chen CM: Fixed point theory for the cyclic weaker Meir-Keeler function in complete metric spaces. Fixed Point Theory Appl. 2012., 2012: Article ID 17Chen CM: Fixed point theorems for cyclic Meir-Keeler type mappings in complete metric spaces. Fixed Point Theory Appl. 2012., 2012: Article ID 41Meir A, Keeler E: A theorem on contraction mappings. J. Math. Anal. Appl. 1969, 28: 326–329. 10.1016/0022-247X(69)90031-6Matkowski J: Integrable solutions of functional equations. Diss. Math. 1975, 127: 1–68.Karapinar E, Romaguera S, Tas K: Fixed points for cyclic orbital generalized contractions on complete metric spaces. Cent. Eur. J. Math. 2013, 11: 552–560. 10.2478/s11533-012-0145-0De Blasi FS, Myjak J: Sur la porosité des contractions sans point fixed. C. R. Math. Acad. Sci. Paris 1989, 308: 51–54.Lahiri BK, Das P: Well-posedness and porosity of certain classes of operators. Demonstr. Math. 2005, 38: 170–176.Popa V: Well-posedness of fixed point problems in orbitally complete metric spaces. Stud. Cercet. ştiinţ. - Univ. Bacău, Ser. Mat. 2006, 16: 209–214. Supplement. Proceedings of ICMI 45, Bacau, Sept. 18–20 (2006)Popa VV: Well-posedness of fixed point problems in compact metric spaces. Bul. Univ. Petrol-Gaze, Ploiesti, Sec. Mat. Inform. Fiz. 2008, 60: 1–4

On the construction of metrics from fuzzy metrics and its application to the fixed point theory of multivalued mappings

[EN] We present a procedure to construct a compatible metric from a given fuzzy metric space. We use this approach to obtain a characterization of a large class of complete fuzzy metric spaces by means of a fuzzy version of Caristi’s fixed point theorem, obtaining, in this way, partial solutions to a recent question posed in the literature. Some illustrative examples are also given.The authors thank the referees for several useful suggestions. Salvador Romaguera and Pedro Tirado acknowledge the support of the Ministry of Economy and Competitiveness of Spain, grant MTM2012-37894-C02-01.Castro Company, F.; Romaguera Bonilla, S.; Tirado Peláez, P. (2015). On the construction of metrics from fuzzy metrics and its application to the fixed point theory of multivalued mappings. Fixed Point Theory and Applications. 2015:226. https://doi.org/10.1186/s13663-015-0476-1S2015:226Kelley, JL: General Topology. Springer, New York (1955)Schweizer, B, Sklar, A: Statistical metric spaces. Pac. J. Math. 10, 314-334 (1960)Klement, E, Mesiar, R, Pap, E: Triangular Norms. Kluwer Academic, Dordrecht (2000)Hamacher, H: Über logische Verknüpfungen unscharfer Aussagen und deren zugehörige Bewertungsfunktionen. In: Progress in Cybernetics and Systems Research, pp. 276-287. Hemisphere, New York (1975)Kramosil, I, Michalek, J: Fuzzy metrics and statistical metric spaces. Kybernetika 11, 326-334 (1975)George, A, Veeramani, P: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395-399 (1994)Gregori, V, Romaguera, S: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115, 485-489 (2000)Radu, V: On the triangle inequality in PM-spaces. STPA, West University of Timişoara 39 (1978)Abbas, M, Ali, B, Romaguera, S: Multivalued Caristi’s type mappings in fuzzy metric spaces and a characterization of fuzzy metric completeness. Filomat 29(6), 1217-1222 (2015)Cho, YJ, Grabiec, M, Radu, V: On Nonsymmetric Topological and Probabilistic Structures. Nova Science Publishers, New York (2006)Hadžić, O, Pap, E: Fixed Point Theory in Probabilistic Metric Spaces. Kluwer Academic, Dordrecht (2001)Mihet, D: A note on Hicks type contractions on generalized Menger spaces. STPA, West University of Timişoara 133 (2002)Mihet, D: A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets Syst. 144, 431-439 (2004)Radu, V: Some fixed point theorems in PM spaces. In: Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol. 1233, pp. 125-133. Springer, Berlin (1985)Radu, V: Some remarks on the probabilistic contractions on fuzzy Menger spaces (The Eighth Intern. Conf. on Applied Mathematics and Computer Science, Cluj-Napoca, 2001). Autom. Comput. Appl. Math. 11(1), 125-131 (2002)Chauhan, S, Shatanawi, W, Kumar, S, Radenović, S: Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces. J. Nonlinear Sci. Appl. 7, 28-41 (2014)Hussain, N, Salimi, P, Parvaneh, V: Fixed point results for various contractions in parametric and fuzzy b-metric spaces. J. Nonlinear Sci. Appl. 8, 719-739 (2015)Mihet, D: Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces. J. Nonlinear Sci. Appl. 6, 35-40 (2013)Hicks, TL: Fixed point theory in probabilistic metric spaces. Zb. Rad. Prir.-Mat. Fak. (Novi Sad) 13, 63-72 (1983)Radu, V: Some suitable metrics on fuzzy metric spaces. Fixed Point Theory 5, 323-347 (2004)O’Regan, D, Saadati, R: Nonlinear contraction theorems in probabilistic spaces. Appl. Math. Comput. 195, 86-93 (2008)Caristi, J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241-251 (1976)Kirk, WA: Caristi’s fixed-point theorem and metric convexity. Colloq. Math. 36, 81-86 (1976)Ansari, QH: Metric Spaces: Including Fixed Point Theory and Set-Valued Maps. Alpha Science, Oxford (2010