h-Preinvex fuzzy processes

• Authors: Matłoka Marian
• Languages of publication: PL EN

Abstracts

EN

We introduce the notion of ℎ -preinvex fuzzy processes. We study their properties and give some inequalities of Hadamard-type for h-convex fuzzy processes.

Keywords

EN

h-preinvex fuzzy process; Hadamard’s inequalities

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Śląski Przegląd Statystyczny
• Year: 2016
• Issue: 14 (20)
• Pages: 27-40

Contributors

author

Matłoka Marian

References

• Aumann R.I., 1965, Integrals of set-valued functions, Journal of Mathematical Analysis and Applications, vol. 12, pp. 1–12.
• Bector C.R., Singh C., 1991, B-vex functions, Journal of Optimization Theory and Applications, vol. 71, pp. 237–253.
• Breckner W.W., 1978, Stetigkeitsaussagen für eine Klasse verallgemeinerter Konvexer Funktionen in topologischen linearen Räumen, Publications de l’Institut Mathématique (Beograd) 23, pp. 13–20.
• Breckner W.W., 1993, Continuity of generalized convex and generalized concave set-valued functions, Revue d’Analyse Numérique ey de Théorie de l’Approximation, vol. 22, pp. 39–51.
• Brunovsky P., 1968, On the necessity of a certain convexity condition for lower closure of control problems, SIAM Journal on Control, vol. 6, pp. 174–185.
• Chalco-Cano Y., Rojas-Medar M.A., 2004, s-Convex fuzzy processes, Computers & Mathematics with Applications, vol 47, pp. 1411–1418.
• Coutat P., 1996, More on continuous closed convex sets, Optimization, vol. 37, pp. 99–112.
• Debreu G., 1983, Mathematical Economics: Twenty Papers of Gerard Debreu, Cambridge University Press, Cambridge–New York.
• Dragomir S.S., 1992, Two mappings in connection to Hadamard’s inequalities, Journal of Mathematical Analysis and Applications, vol. 167, pp. 49–56.
• Dragomir S.S., Fitzpatrick S., 1999, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Mathematica, vol. 32, no. 4, pp. 687–696.
• Hanson M.A., 1981, On sufficiency of Kuhn–Tucker Conditions, Journal of Mathematical Analysis and Applications vol. 80, pp. 545–550.
• Hermes H., 1968, Calculus of set valued functions and control, Journal of Mathematics and Mechanics, vol. 18, pp. 47–60.
• Lowen R., 1980, Convex fuzzy sets, Fuzzy Sets and Systems, vol. 3, pp. 291–310.
• Matłoka M., 1999, Some properties of Φ-convex fuzzy processes, Journal of Fuzzy Mathematics, vol. 7, pp. 701–706.
• Matłoka M., 2000, Convex fuzzy processes, Fuzzy Sets and Systems, vol. 110, pp. 109–114.
• Matłoka M., 2012, A note on (ΦE1, ΦE2)-convex fuzzy processes, Advances in Fuzzy Systems, vol. 2012, article ID 290845.
• Mohan S.R., Neogy S.K., 1995, On invex sets and preinvex functions, Journal of Mathematical Analysis and Applications, vol. 189, pp. 901–908.
• Noor M.S., 2009, Hadamard integral inequalities for product of two preinvex functions, Nonlinear Analysis Forum, vol. 14, pp. 167–173.
• Osuna-Gómez R., Jimenez-Gamero M.D., Chalco-Cano Y., Rojas-Medar M.A., 2004, Hadamard and Jensen inequalities for s-convex fuzzy processes, [in:] Lopez-Diaz M., Gil M.A., Grzegorzewski P., Hryniewicz O., Lawry L. (eds.) Soft Methodology and Random Information Systems, vol. 1, Springer, Heidelberg, pp. 645–652.
• Pini R., Singh Ch., 1997, (Φ1,Φ2)-convexity, Optimization, vol. 40, pp. 103–120.
• Puri M.L., Ralescu D.A., 1987, Fuzzy random variables, Journal of Mathematical Analysis and Applications, vol. 114, pp. 301–317.
• Rockafellar R.T., 1970, Convex Analysis, Princeton University Press, Princeton, NJ.
• Sarikaya M.Z., Saglam A., Yildirim H., 2008, On some Hadamard type inequalities for h-convex functions, Journal of Mathematical Inequalities, vol. 2, pp. 335–341.
• Syau Y.R., Low C.Y., Wu T.H., 2002, A note on convex fuzzy processes, Applied Mathematics Letters, vol. 15, pp. 193–196.
• Varošanec S., 2007, On h-convexity, Journal of Mathematical Analysis and Applications, vol. 326, pp. 303–311.
• Weir T., Mond B., 1988, Preinvex functions in multiobjective optimization, Journal of Mathematical Analysis and Applications, vol. 136, pp. 29–38.
• Youness E.A., 1999, E-convex sets, E-convex functions and E-convex programming, Journal of Optimization Theory and Applications, vol. 102, pp. 439–450