Fixed points for cyclic orbital generalized contractionson complete metric spaces

We prove a fixed point theorem for cyclic orbital generalized contractions on complete metric spaces from which we deduce, among other results, generalized cyclic versions of the celebrated Boyd and Wong fixed point theorem, and Matkowski fixed point theorem. This is done by adapting to the cyclic framework a condition of Meir–Keeler type discussed in [Jachymski J., Equivalent conditions and the Meir–Keeler type theorems, J. Math. Anal. Appl., 1995, 194(1), 293–303]. Our results generalize some theorems of Kirk, Srinavasan and Veeramani, and of Karpagam and AgrawalThe authors are very grateful to the referee since his/her corrections and suggestions have fairly improved the first version of the paper. Salvador Romaguera also acknowledges the support of the Spanish Ministry of Science and Technology, grant MTM2009-12872-C02-01.Karapınar, E.; Romaguera Bonilla, S.; Taș, K. (2013). Fixed points for cyclic orbital generalized contractionson complete metric spaces. Central European Journal of Mathematics. 11(3):552-560. https://doi.org/10.2478/s11533-012-0145-0S552560113Al-Thagafi, M. A., & Shahzad, N. (2009). Convergence and existence results for best proximity points. Nonlinear Analysis: Theory, Methods & Applications, 70(10), 3665-3671. doi:10.1016/j.na.2008.07.022Meir, A., & Keeler, E. (1969). A theorem on contraction mappings. Journal of Mathematical Analysis and Applications, 28(2), 326-329. doi:10.1016/0022-247x(69)90031-6Boyd, D. W., & Wong, J. S. W. (1969). On nonlinear contractions. Proceedings of the American Mathematical Society, 20(2), 458-458. doi:10.1090/s0002-9939-1969-0239559-9Di Bari, C., Suzuki, T., & Vetro, C. (2008). Best proximity points for cyclic Meir–Keeler contractions. Nonlinear Analysis: Theory, Methods & Applications, 69(11), 3790-3794. doi:10.1016/j.na.2007.10.014Jachymski, J. (1995). Equivalent Conditions and the Meir-Keeler Type Theorems. Journal of Mathematical Analysis and Applications, 194(1), 293-303. doi:10.1006/jmaa.1995.1299Jachymski, J. R. (1997). Proceedings of the American Mathematical Society, 125(08), 2327-2336. doi:10.1090/s0002-9939-97-03853-7Anuradha, J., & Veeramani, P. (2009). Proximal pointwise contraction. Topology and its Applications, 156(18), 2942-2948. doi:10.1016/j.topol.2009.01.017Păcurar, M., & Rus, I. A. (2010). Fixed point theory for cyclic -contractions. Nonlinear Analysis: Theory, Methods & Applications, 72(3-4), 1181-1187. doi:10.1016/j.na.2009.08.002Eldred, A. A., & Veeramani, P. (2006). Existence and convergence of best proximity points. Journal of Mathematical Analysis and Applications, 323(2), 1001-1006. doi:10.1016/j.jmaa.2005.10.081Karpagam, S., & Agrawal, S. (2011). Best proximity point theorems for cyclic orbital Meir–Keeler contraction maps. Nonlinear Analysis: Theory, Methods & Applications, 74(4), 1040-1046. doi:10.1016/j.na.2010.07.026Karapınar, E. (2011). Fixed point theory for cyclic weak ϕ-contraction. Applied Mathematics Letters, 24(6), 822-825. doi:10.1016/j.aml.2010.12.01

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

Inactivation of the indole-diterpene biosynthetic gene cluster of Claviceps paspali by Agrobacterium-mediated gene replacement

The hypocrealean fungus Claviceps paspali is a parasite of wild grasses. This fungus is widely utilized in the pharmaceutical industry for the manufacture of ergot alkaloids, but also produces tremorgenic and neurotoxic indole-diterpene (IDT) secondary metabolites such as paspalitrems A and B. IDTs cause significant losses in agriculture and represent health hazards that threaten food security. Conversely, IDTs may also be utilized as lead compounds for pharmaceutical drug discovery. Current protoplast-mediated transformation protocols of C. paspali are inadequate as they suffer from inefficiencies in protoplast regeneration, a low frequency of DNA integration, and a low mitotic stability of the nascent transformants. We adapted and optimized Agrobacterium tumefaciens-mediated transformation (ATMT) for C. paspali and validated this method with the straightforward creation of a mutant strain of this fungus featuring a targeted replacement of key genes in the putative IDT biosynthetic gene cluster. Complete abrogation of IDT production in isolates of the mutant strain proved the predicted involvement of the target genes in the biosynthesis of IDTs. The mutant isolates continued to produce ergot alkaloids undisturbed, indicating that equivalent mutants generated in industrial ergot producers may have a better safety profile as they are devoid of IDT-type mycotoxins. Meanwhile, ATMT optimized for Claviceps spp. may open the door for the facile genetic engineering of these industrially and ecologically important organisms.</p

Regenerative potential, metabolic profile, and genetic stability of Brachypodium distachyon embryogenic calli as affected by successive subcultures

Brachypodium distachyon, a model species for forage grasses and cereal crops, has been used in studies seeking improved biomass production and increased crop yield for biofuel production purposes. Somatic embryogenesis (SE) is the morphogenetic pathway that supports in vitro regeneration of such species. However, there are gaps in terms of studies on the metabolic profile and genetic stability along successive subcultures. The physiological variables and the metabolic profile of embryogenic callus (EC) and embryogenic structures (ES) from successive subcultures (30, 60, 90, 120, 150, 180, 210, 240, and 360-day-old subcultures) were analyzed. Canonical discriminant analysis separated EC into three groups: 60, 90, and 120 to 240 days. EC with 60 and 90 days showed the highest regenerative potential. EC grown for 90 days and submitted to SE induction in 2 mg L−1 of kinetin-supplemented medium was the highest ES producer. The metabolite profiles of non-embryogenic callus (NEC), EC, and ES submitted to principal component analysis (PCA) separated into two groups: 30 to 240- and 360-day-old calli. The most abundant metabolites for these groups were malonic acid, tryptophan, asparagine, and erythrose. PCA of ES also separated ages into groups and ranked 60- and 90-day-old calli as the best for use due to their high levels of various metabolites. The key metabolites that distinguished the ES groups were galactinol, oxaloacetate, tryptophan, and valine. In addition, significant secondary metabolites (e.g., caffeoylquinic, cinnamic, and ferulic acids) were important in the EC phase. Ferulic, cinnamic, and phenylacetic acids marked the decreases in the regenerative capacity of ES in B. distachyon. Decreased accumulations of the amino acids aspartic acid, asparagine, tryptophan, and glycine characterized NEC, suggesting that these metabolites are indispensable for the embryogenic competence in B. distachyon. The genetic stability of the regenerated plants was evaluated by flow cytometry, showing that ploidy instability in regenerated plants from B. distachyon calli is not correlated with callus age. Taken together, our data indicated that the loss of regenerative capacity in B. distachyon EC occurs after 120 days of subcultures, demonstrating that the use of EC can be extended to 90 days